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Formulate All
Objective
Formulate
\min \sum_{b=1}^{B} BinUsed_b
Confidence:
5/5
min
∑
b
=
1
B
B
i
n
U
s
e
d
b
\min \sum_{b=1}^{B} BinUsed_b
min
b
=
1
∑
B
B
in
U
se
d
b
Constraints
Formulate
\sum_{i=1}^{N} ItemInBin_{i,b} \times ItemSizes_i \leq BinCapacity \times BinUsed_b, \quad \forall b = 1, \ldots, B
Confidence:
5/5
∑
i
=
1
N
I
t
e
m
I
n
B
i
n
i
,
b
×
I
t
e
m
S
i
z
e
s
i
≤
B
i
n
C
a
p
a
c
i
t
y
×
B
i
n
U
s
e
d
b
,
∀
b
=
1
,
…
,
B
\sum_{i=1}^{N} ItemInBin_{i,b} \times ItemSizes_i \leq BinCapacity \times BinUsed_b, \quad \forall b = 1, \ldots, B
i
=
1
∑
N
I
t
e
m
I
n
B
i
n
i
,
b
×
I
t
e
m
S
i
ze
s
i
≤
B
in
C
a
p
a
c
i
t
y
×
B
in
U
se
d
b
,
∀
b
=
1
,
…
,
B
Formulate
\sum_{b=1}^{B} ItemInBin_{i,b} = 1, \quad \forall i \in \{1, 2, \ldots, N\}
Confidence:
5/5
∑
b
=
1
B
I
t
e
m
I
n
B
i
n
i
,
b
=
1
,
∀
i
∈
{
1
,
2
,
…
,
N
}
\sum_{b=1}^{B} ItemInBin_{i,b} = 1, \quad \forall i \in \{1, 2, \ldots, N\}
b
=
1
∑
B
I
t
e
m
I
n
B
i
n
i
,
b
=
1
,
∀
i
∈
{
1
,
2
,
…
,
N
}
Formulate
ItemSizes[i] \geq 0, \quad \forall i \in \{1, 2, \ldots, N\}
Confidence:
5/5
I
t
e
m
S
i
z
e
s
[
i
]
≥
0
,
∀
i
∈
{
1
,
2
,
…
,
N
}
ItemSizes[i] \geq 0, \quad \forall i \in \{1, 2, \ldots, N\}
I
t
e
m
S
i
zes
[
i
]
≥
0
,
∀
i
∈
{
1
,
2
,
…
,
N
}
Formulate
\sum_{b=1}^{B} BinUsed_{b} \geq 0
Confidence:
5/5
∑
b
=
1
B
B
i
n
U
s
e
d
b
≥
0
\sum_{b=1}^{B} BinUsed_{b} \geq 0
b
=
1
∑
B
B
in
U
se
d
b
≥
0
Variables
Symbol
Shape
Definition
Domain
BINARY
INTEGER
CONTINUOUS
BINARY
INTEGER
CONTINUOUS
BINARY
INTEGER
CONTINUOUS
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